Question: Write the equation of a line that is parallel to ${y=-\dfrac{3}{2}x-1}$ and that passes through the point ${(4,6)}$.
Solution: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Slope of the given line: ${-\dfrac{3}{2}}$ Slope of the parallel line: $C{-\dfrac{3}{2}}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{-\dfrac{3}{2}}$ and pass through the point ${(4,6)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{6} &= C{-\dfrac{3}{2}}(x-{4})\\\\\\ y-6 &= C{-\dfrac{3}{2}}x +6 \\\\\\ y &= C{-\dfrac{3}{2}}x {+12} \end{aligned}$ Answer The equation of the parallel line is $y = C{-\dfrac{3}{2}}x {+ 12}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${10}$ ${12}$ ${14}$ ${\llap{-}4}$ $y$ $x$